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Let's consider the Option Chain for the Stock. There are two 3D surfaces representing the probability of the future stock price and the option prices. I wonder if they are representing the same thing?

3D Option Surface: there's the set of PUTs and CALLs options, with different expiration, strikes, and premium. This set of options form 3D surface, with x - time, y - strike, z - premium.

3D Future Price Probability Surface: probability surface of the future stock prices. With x - time, y - possible price and z - density (probability of the given price at a given time).

And it seems those surfaces are "equal":

  • It's possible to compute Option Surface from Future Price Surface. By running Monte Carlo over Future Price Probability Surface and computing the premium for every PUT and CALL option strike.
  • It's possible to compute Future Price Probability Surface from the Option Surface. By trying all the possible Future Price Probability Surfaces, until we find the one that if used for computing the option prices - give prices closest to our Option Surface.

Does that means that option pricing methods are kinda the same as methods for future price prediction? And thus the ML technics like RNN for future price prediction are also could be used in Option Pricing. And technics like Black-Scholes are just a fancy way to predict stock prices?

P.S.

I'm not talking about the Volatility Surface - because as far as I know (maybe I'm mistaken) the Volatility Surface - is abstract surface representing some parameters in Black-Scholes and not real options. I'm talking here about the real surface formed by real option attributes.

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    $\begingroup$ The volatility surface is the option price surface.. $\endgroup$ – ilovevolatility May 31 at 14:10
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Q: Does that means that option pricing methods are kinda the same as methods for future price prediction?

A: Yes. Option price is equal to the expectation of discounted payoff.

Q: And thus the ML technics like RNN for future price prediction are also could be used in Option Pricing.

A: Yes. But whether it is useful is another story.

Q: And technics like Black-Scholes are just a fancy way to predict stock prices?

A: Black-Scholes is a way to model the stock price process. If one would like to predict stock price distribution using Black-Scholes, one needs to have an estimation of the volatility parameter.

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